A path integral Monte Carlo method for R\'{e}nyi entanglement entropies

TL;DR

This paper introduces a path integral Monte Carlo algorithm to measure Re9nyi entanglement entropies in interacting bosonic systems, enabling analysis of quantum correlations in continuum models relevant to experiments.

Contribution

The paper presents a novel quantum Monte Carlo method for calculating Re9nyi entanglement entropies in continuum interacting bosons, applicable in any spatial dimension.

Findings

Successfully benchmarked against an exactly solvable 1D model.

Demonstrated ability to compute various types of entanglement.

Retains polynomial scaling for sign-problem-free models.

Abstract

We introduce a quantum Monte Carlo algorithm to measure the R\'enyi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability and interactions. We present proof-of-principle calculations, and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large scale many-body systems of interacting bosons.